Life on Mars and why the Logic Implication cannot be T,F,T,T #1468 Correcting Math

Now earlier today I gave the example of Pagels with his demon that turns off the 4 forces of physics and discussing what happens to Nature when one is turned off. I wrote that Pagels could do that in Old Logic where they had the Logic Implication all wrong and messed up with T,F,T,T when it should be T,F,undefined,undefined. When Logic Implication is correct then when a demon turns off the EM force or any of the 4 forces, the only logical conclusions that are valid is that all of Physics no longer exists. With true correct logic tables of Implication, we can only deduce that all of physics is gone if any one of its four forces is gone, because they are interconnected and not separate.

When you have a messed up table of implication, you would easily mess up many or most every deduction you have.

Now I said earlier that the best common sense description of implication is the phrase "Growing to Become Larger as". So that when we have a P--> Q we can replace that by P growing to become larger as Q. So a T can grow to become a larger T, but a T can never grow to become a larger F. Nor can a F ever grow to become a T, never mind a larger T. But, can a F grow to become a larger F? It may sound as though the fourth line of the truth table of Implication has a ring of truth to it that we would have T,F, undefined, T.

So, do we need just one undefined in Implication and have three lines of T or F? I say no, because a falsehood does not grow into a larger falsehood. Truth is science and science is the laws of physics and the experiments of physics. Falsehood is not understanding of science and are static objects.

I say no, because of mathematics. We need a value for 2/0 (2 or any number other than 0), and a value for 0/0 which takes up two of those implication lines.

So let me show how and why I think Implication should be T,F,undefined,undefined and not that of T,F, undefined, T.

Take the question of life on Mars. Does life exist on Mars. The question is different from "has life ever existed on Mars?" It could have been that Mars had life a long time ago, but all perished.

So, a implication truth table of T, F, undefined, undefined would have us say that no life exists on Mars if no present life exists checking most of the planet and where no evidence of past life arises. If we had a truth table of T,F,T,T or T,F, undefined, T, then we can say life exists on Mars if we find a tiny shred of evidence such as amino acids. When you leave the last two lines undefined in implication, you require the most stringent of logic to assert the truth of a question. When you leave the last two lines or the fourth line as T, you then make lax of science and just the nit bit of evidence allows you to claim that life exists on Mars, when it truly does not.

Logic with Implication of T,F, undefined, undefined is the most strict logic possible, and is what science and physics and mathematics demands. Logic with T,F,T,T or with T,F, undefined,T, is a logic that allows science fiction to run rampant in science and mathematics.

So how does one prove that Mars has life or does not have life? Proof in science is by experiment and observation, and proof in mathematics is by logical deduction. To prove Mars has life is simply to find it and show it. To prove Mars has no life is more difficult, for you have to cover the surface in a meaningful way, take samples, take many observations. And just because you find amino acids or find what appears to be some "track" is no proof under T,F,undefined, undefined but is proof under the Old Logic of T,F,T,T. It is proof under Old Logic, because falsehoods can grow to become truths.